Can anyone explain how a neutral wire supposedly doesn't have any voltage even though you can't have current (precisely because of the difference in electron count from one area to another) without it? Doesn't the neutral switch to the line half of the time? Also, how can you drop voltage when going through a resistance, don't you still have the same amount of force working on each electron in close proximity severely repelling each other, which is voltage?

To your first question,in practice a neutral wire as any other resistance does generate a random noise (white gaussian noise) on its ends. The average of this voltage is zero but its variance(rms voltage) is non-zero.
Concerning the voltage drop on resistance may be you should look at "Drude model" (metal like a gas of electrons), try wikipedia.
Does this help?

The neutral wire is the return for current. Measure from neutral to ground and the voltage in the neutral line should always be very close to zero. It is the polarity of the hot wire that goes from positive to negative periodically. It is the voltage in the hot wire that drives current.

Electrons do repel because of like charges, but it's not a lot of force. Look into the space charge around the plate of a vacuum tube to get a feel for that. In a CRT, a force of 25,000 volts can pull an electron into a phosphor hard enough for it to emit a photon and so shed the excess energy. The electrostatic focusing lens that keeps the electron beam from spreading does so with a potential of a 1 - 300 volts. Electrons get pushed around easily.

Looked at another way, when a conductor connects two points with a difference of potential, the force that moves electrons that are close to the terminals causes all the electrons to move with them because that repelling force makes them want to keep that spacing. If one moves left, everybody else does, too.

Voltage is the result of a difference in charge. The positive terminal of a battery is deficient in electrons and the negate terminal has a surplus of electrons, both conditions produced by the chemical reaction in the battery.

Neutral is a term used in multi phase systems. when you have a neutral between phases, and the phase loads are balanced, there is no potential differential placed on the neutral, as the potential exsists across the phases. However, if the loads are unbalanced, you will now have a potential, and flow, within the neutral.

I still can't see how the neutral has no voltage. I can see how there won't be any voltage between ground and neutral, but not the hot and neutral. Can someone start at the source and explain what happens? I thought electrons would be forced to move in one side, other electrons would move out of the way, and so on. Just like water in a higher tank would flow to a lower tank, like the explanation says. If this is not true then all of the books need to be corrected.